# Related objects

Show commands for: Magma / SageMath

## Decomposition of $S_{8}^{\mathrm{new}}(9)$ into irreducible Hecke orbits

magma: S := CuspForms(9,8);
magma: N := Newforms(S);
sage: N = Newforms(9,8,names="a")
Label Dimension Field $q$-expansion of eigenform
9.8.1.a 1 $\Q$ $q$ $\mathstrut-$ $6q^{2}$ $\mathstrut-$ $92q^{4}$ $\mathstrut-$ $390q^{5}$ $\mathstrut-$ $64q^{7}$ $\mathstrut+$ $1320q^{8}$ $\mathstrut+O(q^{10})$
9.8.1.b 2 $\Q(\alpha_{ 2 })$ $q$ $\mathstrut+$ $\alpha_{2} q^{2}$ $\mathstrut+$ $232q^{4}$ $\mathstrut-$ $16 \alpha_{2} q^{5}$ $\mathstrut+$ $260q^{7}$ $\mathstrut+$ $104 \alpha_{2} q^{8}$ $\mathstrut+O(q^{10})$

The coefficient fields are:

Coefficient field Minimal polynomial of $\alpha_j$ over $\Q$
$\Q(\alpha_{ 2 })\cong$ $\Q(\sqrt{10})$ $x ^{2}$ $\mathstrut -\mathstrut 360$

## Decomposition of $S_{8}^{\mathrm{old}}(9)$ into lower level spaces

$S_{8}^{\mathrm{old}}(9)$ $\cong$ $\href{ /ModularForm/GL2/Q/holomorphic/3/8/1/ }{ S^{ new }_{ 8 }(\Gamma_0(3)) }^{\oplus 2 }$